Hello and welcome to the forums
HD 4870 performs better(not much)but its noiser,has more power consumption and its hotter on the other hand HD 5770 performs a little lower but has newer technologies like DX11 and runs cooler and quieter
Dual 5770's hands down. DirectX 11, runs quieter, cooler and draws less power than the 4870's. 4870's perform better, but not by much and with going Crossfire on the 5770's, you'll have a screaming gaming machine.
I'd take a single HD5850 over 2 HD5770s. Always smart to go for a more powerful single card to start with rather than crossfiring weaker ones. The HD5850s OCing ability makes the performance difference negligible.
I would definitely go for 5770's over 4870's. There is no question when you think of where games are heading (into DX11 and multi-monitor gaming etc.) and how long 5770's will last as opposed to 4870's, not to mention heat or power consumption. The performance gap has also been coming down as the drivers for the 5770 are maturing as well.
All that being said, a single 5850 is almost the same price (even a few $$ cheaper now) and will last even longer since you'll then be able to drop a second one in there later.